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2d
asked A smooth function which is nowhere real analytic, and preserves rationality of its argument
Apr
7
awarded  Good Question
Mar
23
awarded  Nice Answer
Mar
22
comment Is it possible to formalize all mathematics in terms of ordinals only?
@HanulJeon Of course, there are variants of set theory, where not every set admits a well-ordering, and they constitute an important and interesting part of infinitary mathematics. But for the positive answer to my question, it is sufficient if we can model those variants of set theory in the theory of ordinals.
Mar
18
comment What's the difference between ${\{a}\}$ and $a$?
@PedroSánchezTerraf My bad. Fixed. Thanks!
Mar
18
revised What's the difference between ${\{a}\}$ and $a$?
deleted 22 characters in body
Mar
17
answered What's the difference between ${\{a}\}$ and $a$?
Mar
17
asked Is it possible to formalize all mathematics in terms of ordinals only?
Mar
16
comment Obscuring squares of Rubik's cube
@Matta Yes, we can assume the color scheme is known.
Mar
14
awarded  Nice Answer
Mar
14
comment Obscuring squares of Rubik's cube
To establish a simple lower bound we can reason as follows. Suppose we obscured $9$ squares, all of the same color (say, red). By inspection, we can see that $9$ red squares are not visible anywhere, but there are $9$ obscured squared. So, we can deduce that all obscured squares are red. Hence, no information is lost, and no states were made indistinguishable. We can furthermore obscure a non-red square on a corner cubie with a red square. By inspection of other corner cubies, we can find what color has been obscured, and the last visible square is enough to infer the orientation of the cubie.
Mar
13
revised Obscuring squares of Rubik's cube
added 234 characters in body
Mar
12
revised Obscuring squares of Rubik's cube
added 214 characters in body
Mar
12
revised Obscuring squares of Rubik's cube
added 214 characters in body
Mar
12
asked Obscuring squares of Rubik's cube
Mar
12
awarded  Necromancer
Mar
12
comment Relations between definite integrals not having a known closed form
@YuriyS (cont'd) So, it is not some set of functions fixed forever, but rather depends on the current state of mathematical knowledge. Usually, new functions are defined from their integral representations or series, or as solutions to differential or functional equations. Once we have a notation for a new function, and some transformation rules and connections to other functions, which prove to be useful, and are being used in further research by mathematicians other than the original inventor, then, I think, expressions in terms of this function deserve to be called closed-form expressions.
Mar
12
comment Relations between definite integrals not having a known closed form
@YuriyS Indeed, it is not a precise term, but I would consider a number to have a closed form, if it can be expressed using algebraic numbers, elementary functions, known mathematical constants and known special functions. Again, "known" is a rather vague term, but I would consider a constant or special function known, if it has an established name(s), and there has been some research about it: some theorems proved about it, some relations to other previouly known functions and constants found. Usually, it has to be mentioned in a mathematical book or in several papers (by more than 1 author).
Mar
11
awarded  Nice Question
Mar
7
comment A possible alternative to the Axioms of Pair, Union, Infinity and Replacement
@AsafKaragila Yes, you are right. My mistake.